Big Idea:
Being able to understand and explain numbers will help students make sense of multi-digit computation and problem solving.

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using an array model.

Task 1: 6 x 5

For the first task, I asked students for the solution. They said, "30!" Then I said: Okay, great! Now show me how 6x5=30! Sometimes we focus so much on getting the correct answer that this takes attention away from carefully modeling our thinking. Immediately, students got right to work: Students Trying Multiple Strategies. I loved watching one student explain how she Decomposed 6x5=2(3x3)+2(3x2). This same student struggled with this concept a few days ago. Her understanding has of decomposing and modeling a multiplication expression has clearly grown! By the time we were finished with this problem, almost all students had Multiple Strategies for 6 x 5.

Task 2:36 x 5

During the next task, 36x5, I worked closely with a student who struggles with math: Supporting a Struggling Student. To help him understand how to decompose the 36, I showed him 16 = 10 + 6 and asked him to decompose 26 and then 36. This really helped. Then, I drew an array and asked him to use the array to solve 36 x 5. When we got to 5 x 10, I modeled a simpler problem, 1 x 10, and then asked him to solve 2 x 10... 3 x 10... all the way up to 5 x 10. During our share time, he then shared his work with the class: A Proud Moment!.

Task 3:136 x 5

When solving 136 x 5, some students decomposed one multiplicand while others decomposed both the 136 and the 5: 136x5.

To begin, I invited students to get their math journals and meet me on the carpet. I then introduced the Goal: I can represent numbers in written form. Throughout this lesson, I will use the terms "written form" and "word form" interchangeably as I want students to view them as synonymous terms.

Forms of Numbers:

I explained: Do you remember yesterday when we talked about the three basic ways to represent numbers? The first way is called standard form. I presented the poster for Standard Form. Next, we have Expanded Form, and the last form is called Word Form. Prior to the lesson, I created each of these posters knowing that we could refer to them the rest of the year.

When reviewing expanded form, I wanted to deepen student understanding of expanded form by using four different colored strips of paper (similar to arrow cards) to show 2000 (green paper) + 500 (red paper) + 30 (yellow paper) + 2 (pink paper). This Expanded Form Demonstration really helped many students grasp the idea of expanded form. Some students responded, "Oh! Now I get it!"

Once we got to word form, I explained: Word form is a way to write numbers using words. For example, 2,532 would be written this way: two thousand, five hundred thirty-two. When teaching students how to write numbers in word form, there are three key concepts I always try to cover: 1. comma placement, 2. spelling of numbers, and 3. hyphen placement.

1. Comma Placement

To teach students the proper way to place commas in a number, I used following place value magnets to demonstrate comma placement on the board: Place Value Magnets & Comma Placement. I explained: Whenever we write numbers, we use commas to separate the periods in the place value chart. For example, we use a comma to separate the millions and thousands period. We also use a comma to separate the thousands and ones period. Here's an example: We would write 2,500,003 with two commas: two million, five hundred thousand, three. So if we just have 500,003, we only need one comma: five hundred thousand, three.

2. Spelling of Numbers

We then moved on to the spelling of numbers. I showed students the Spelling of Numbers Chart I had created prior to the lesson. I set high expectations by asking students to make sure every word is spelled correctly today!

3. Hyphen Placement

While looking at the Spelling of Numbers Chart, I asked students to observe which numbers have hyphens (or a dash). I asked questions to help students differentiate between numbers with a hyphen and numbers without: Does the number five have a hyphen? (no) How about the number eighteen? (no) Does sixty have a hyphen? (no) How about ten thousand? (no) Which numbers do have hyphens then? Students responded, "Only numbers like twenty-four." What other numbers require a hyphen? Student responses varied: "Sixty-six..." "Ninety-four... "Thirty-five..." Okay, so we use a hyphen with all numbers between 21 and 99, except with the multiples of 10, like thirty, forty, fifty...?

Resources

At this point, I asked students to create a three column in their math journals with the following headings: Standard Form, Expanded Form, and Written Form. I wanted to connect written form with prior learning. Here's what the chart will look like when we are finished with this activity: Standard, Expanded, Written Forms Chart.

I then asked, What is the standard form for this number? Referring to the standard form poster, I asked: How would you write the number 2 using the digits 0-9? Students responded, "Just write 2!" I wrote the number 2 in the Standard Form column of the chart.

3. Expanded Form:

I continued: Let's look at the expanded form. Referring to the expanded form poster, I asked: How would you write 2 using the value of each digit? Students responded 2 in almost an annoyed way! They were anxious to be challenged! I always start with easy tasks and work up to more complex tasks to build a staircase of complexity!

4. Word Form:

Referring to the written form poster, I asked: How would you write the number 2 using words? One student said, "T...w...o."

More Complex Numbers

Students were clearly ready to move on to more difficult tasks! One step at a time, I continued building the learning progression. We continued the same steps: 1. Place Value Blocks, 2. Standard Form, 3. Expanded Form, and 4. Written Form using the numbers listed below.

I gradually released responsibility by asking students to complete their own charts in their student journals and to turn and talk with a partner before discussing the forms of each number as a class. I also used similar digits to reinforce number sense (112 = 12 + 100 more).

Flipping the Order of Tasks

For the last four tasks in the Standard, Expanded, Written Forms Chart, I provided the word forms for all four numbers at one time instead of modeling the number with place value blocks one at a time. This gave me more time to conference with struggling students. Also, I wanted to make sure students were able to interpret the written form of larger numbers.

As students finished, I asked for volunteers to complete the Standard and Expanded Form columns on the whiteboard in front of the class. Here, students explain the Standard & Expanded Forms for 72,072.. I ask questions to encourage student engagement and higher level thinking.

When writing the number, 522,004, some students struggled with representing a number with zeros. This student explained to the rest of the class how 522,004 would look if we interpreted it as 5,224: Understanding the Written Form for 522,004.

During this time, I checked on each student and provided support and questioning as needed. Two students in particular needed extra support so I pulled them back up to the white board for individualized instruction. I'll address these students in the reflection section.

Most students finished within 15 minutes! I asked students to check their answers with peers. Peer-checking gives students the opportunity to practice Math Practice 3: Construct viable arguments and critique the reasoning of others. Here are examples of proficient students: Writing Numbers for Word Names and Writing Word Names for Numbers.